Find the n-th term of the sequence 3, 7, 11, 15, ...

**The reasoning** This is an **arithmetic sequence** — the difference between consecutive terms is constant. Let's check: 7 − 3 = 4, 11 − 7 = 4, 15 − 11 = 4. The common difference is **4**. The formula for the n-th term of an arithmetic sequence is: **Tₙ = a + (n − 1)d** where a = first term (3) and d = common difference (4). So: Tₙ = 3 + (n − 1)4 = 3 + 4n − 4 = **4n − 1** Let's verify: When n = 1: 4(1) − 1 = 3 ✓ When n = 2: 4(2) − 1 = 7 ✓ When n = 3: 4(3) − 1 = 11 ✓ **Why the wrong options tempt you** - **4n** looks close because you see the "4" in the difference, but it gives 4, 8, 12... — all one more than our sequence. - **n + 4** comes from seeing "add 4 each time" but ignores you're *multiplying* by position. - **n² − 1** gives 0, 3, 8, 15... — wrong from the start. **Quick takeaway** In arithmetic sequences, the n-th term is **(first term) + (n − 1) × (common difference)** — always simplify to check!